GCF of 403/865, 9971/225
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 403/865, 9971/225 i.e 13/38925 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/865, 9971/225.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 403/865,9971/225?
Given fractions are 403/865,9971/225
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 403/865,9971/225, numerators are 403,9971
Denominators are 865,225
The GCF of 403,9971 is 13 .
LCM of 865,225 is 38925.
The greatest common factor of 403/865,9971/225 = [GCF of 403,9971]/[LCM of 865,225]= 13/38925
Therefore, the GCF of 403/865,9971/225 is 13/38925.
To find the highest common factor of 403,9971, we have to find the factors of both numbers and list the highest common factor.
The factors of 403 are 1, 13, 31, 403
The factors of 9971 are 1, 13, 59, 169, 767, 9971
The HCF of 403,9971 is 13.
Lets's calculate GCF of 403,9971
| 13 | 403, 9971 |
| 31, 767 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 403,9971 By Matching Biggest Common Factor Method
Now, list down the factors of 403
:1,13,31,403
Now, list down the factors of 9971
:1,13,59,169,767,9971
Greatest Common Factor
We found the factors 403,9971 . The biggest common factor number is the GCF number.
So the greatest common factor 403,9971 is 13.
Lets's calculate LCM of 865,225
| 5 | 865, 225 |
| 173, 45 |
∴ So the LCM of the given numbers is 5 x 173 x 45 = 38925
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/38925
Therefore, the GCF of Fractions 403/865,9971/225 is 13/38925
Least Common Multiple of 865,225 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 865,225 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(865,225) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(865,225) x common factors =5 x 1 = 5
LCM(865,225) = ( 865 × 225 ) / 5
LCM(865,225) = 194625 / 5
LCM(865,225) = 38925
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 403/865, 9971/225
1. What is the HCF of 403,9971?
The HCF of 403,9971 is 13
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 403/865, 9971/225?
Answer: GCF of Numerators as per given numbers 403/865, 9971/225 is
GCF of Numerators i.e. for 403,9971 is 13
LCM of denominators i.e. for 865,225 is 38925.
Thus, GCF of Fractions is 13/38925.Finally, GCF of Fractions for 403/865, 9971/225 is 13/38925.